Orthogonal rational functions


Adhemar Bultheel       Pablo González-Vera       Erik Hendriksen       Olav Njåstad

[ORF IMAGE 1] ORF [ORF IMAGE 2]



Abstract: This book generalizes the classical theory of orthogonal polynomials on the complex unit circle or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. This theory has many applications both in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

[ORF IMAGE 3] Table of Contents
  1. Preliminaries
  2. The fundamental spaces
  3. The kernel functions
  4. Recurrence for orthogonal functions
  5. Quadrature
  6. Interpolation
  7. Density of the rational functions
  8. Favard theorems
  9. Convergence
  10. Moment problems
  11. The boundary case
  12. Some applications
[gang of 4] From left to right
  • Erik Hendriksen
  • Adhemar Bultheel
  • Pablo González Vera
  • Olav Njåstad
Antwerp 1999

Status:
Published: volume 5 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 1999. ISBN: 0 521 65006 2.

BiBTeX entry: 

   @book{BooksBGHN99,
      author = "A. Bultheel and P. Gonz{\'a}lez-Vera and E. Hendriksen and O. Nj{\aa}stad",
      title = "Orthogonal rational functions",
      year = "1999",
      series ="Cambridge Monographs on Applied and Computational Mathematics",
      volume = "5",
      publisher = "Cambridge University Press",
      url = "http://nalag.cs.kuleuven.be/papers/ade/ORF/index.html",
      isbn = "0-521-65006-2 (hb) 978-0-521-11591-9 (pb)",
      LIRIAS = "134368",
      ZBL = "923.42017",
      MR = "2000c:33001",
   }

Files:
Introduction and table of contents Compressed PostScript (.ps.gz) ( 63K),

Publisher's information
Amazon.com here
LCCN 98011646

Errata are available in [html] [tex] [pdf] [ps] [dvi]
Last update: Wednesday 14 April 2010, 10:24:57 AM CEST.


Java applet:
You actually want to see some ORFs?
Complex functions in full colour like the ones on top of this page.
They are available via a Java-applet.
A brief summary of the theory and a link to the java applet are available here

Adhemar Bultheel <Adhemar.Bultheel at cs.kuleuven.be>